All Questions
Tagged with molecular-orbital-theory physical-chemistry
75 questions
2
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Symmetry and angular momentum in the Jahn-Teller paper
In the original paper of Jahn et Teller (https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1937.0142, section I-Two Examples) are described two examples: a linear molecule and one with square ...
- 177
3
votes
0
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94
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How do I derive the second-order mixing coefficient from Perturbational Molecular Orbital (PMO) Theory?
Hi I need help deriving a result from the PMO theory. I'm currently reading the second edition of the book Orbital Interactions in Chemistry by Thomas A. Albright, Jeremy K. Burdett & Myung-Hwan ...
- 51
0
votes
1
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102
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How do you write the electron configuration using gerade and ungerade notations?
My textbook shows the higher energy bonding and antibonding orbitals, and starts naming them from $1\sigma_\mathrm u.$
I don't think this is correct and it's really confusing me. What can I write if a ...
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0
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81
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How accurate is the Molecular Orbital Theory
When you take it to its core, when forming a covalent bond, which is more accurate, the MO theory with idea of electron behaving as waves and superimposition, and idea of forming Molecular orbitals ...
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2
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0
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117
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Can you tell if a HOMO to LUMO transition is allowed just by picturing the MOs?
Someone told me that they said the HOMO to LUMO transition is allowed in benzene and naphthalene just by looking at the MOs and without using the irreps for each orbital and the character tables?
How ...
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8
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2
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833
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Mulliken Labels: How do I tell apart E, doubly degenerate, symmetry apart from T, triply degenerate, symmetry for a molecular orbital?
With A and B, it's pretty simple. If you rotate the molecule about its principle axis to where the orbitals line up, and the signs change, it's Mulliken label has a B. otherwise, it's A.
I heard E ...
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0
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288
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Why is cyclohexane more polarizable than benzene?
Looking at figure 4.2 here, we can see experimentaly that cyclohexane is more polarizable than benzene.
Why is this the case?
Intuitively, I would think that because the orbitals in benzene are more ...
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-1
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1
answer
114
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Table of molecular orbital extents — what does it even mean? [closed]
In molecular orbital theory, the term molecular orbital extents was mentioned, although I can't really picture it. Does molecular orbital extent refer to the spatial distribution of electrons in a ...
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3
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1
answer
322
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Is there a difference between Hartree-Fock method and LCAO?
I have to dive in some quantum chemistry for a quantum machine learning project and I came across the so-called Hartree-Fock method.
In one of the reference I used, they considered electrons as ...
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2
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0
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36
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LCAO-MO ansatz for arbitrary hydrogenic molecule term
I am struggling to understand the connection between molecular electronic term symbols and translating the symmetries to the underlying wavefunction.
In particular, my understanding of the LCAO-MO ...
- 284
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2
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409
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Molecular orbital mixing in second period elements
Why do the $\pi_u(2p)$ and $\sigma_g(2p)$ diatomic MO mix within the second period elements as it's shown in the image below?
user126892
9
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2
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753
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Bonding in hypervalent molecules
I don't know where they go the electrons of the extended-valence in molecules like $\ce{SF6}$ or $\ce{PCl5}$ for instance because my teacher said that the d orbitals can't interact with s and p (or ...
- 691
4
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1
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160
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pKa of methylene protons in cycloheptatriene vs cyclopropene
The $\mathrm{p}K_\mathrm{a}$ values of methylene protons in cycloheptatriene vs cyclopropene are found to be 60 and 36, respectively.
From what I understand - both conjugate bases are non-aromatic (...
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3
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1
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234
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Can two noble gases attract each other?
If two hydrogen atoms are far apart, they have no effect on one another. But as they are bought closer together, they begin to excerpt an effect. The two nuclei, having the same positive charge, repel ...
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Why are HOMO and LUMO energies invariant under spin-flip?
Atomic theory says singlet and triplet energies for the same orbital differ because of exchange interaction. However, molecular orbital (MO) theory describes the energy between the HOMO (highest ...
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440
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Does the 1s orbital have two different phases? [duplicate]
How can the 1s orbital (in H atom for example) interfere both constructively and destructively (to give rise to bonding and antibonding molecular orbitals) with another 1s orbital, if the 1s orbital ...
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2
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Molecular orbitals in an ionic diatomic compound
The wavefunction of a heteronuclear diatomic molecule, after the orbital approximation and the Born-Oppenheimer approximation, is
$$\psi = c_A \chi_A \pm c_B \chi_B $$
where $\chi$ are the starting AO ...
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1
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93
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Relation of partial charge with wavefunction
Suppose we have an one electron system. The probability $P$ that electron's position is in some interval $x + dx$ is given by:
$$P = \int_x^{x+dx}|Ψ(x)|^2 dx$$
So if we measure $N$ times the electron'...
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1
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80
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Do different types of MOs have different occupancies?
There was a question in my textbook regarding the number of electrons in a molecular orbital.
The maximum number of electrons in a sigma, pi, and delta molecular orbital are respectively?
Now, I ...
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2
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Is strength of pi bonds greater than sigma bond of nitrogen molecule?
I am referring to molecular orbital (MO) theory. In the nitrogen molecule (and elements of lower atomic number) $\textrm{sp}$ mixing occurs and the sigma orbital set is raised above the pi orbital set....
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2
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913
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Spin Multiplicities of Ions
The multiplicity is fundamentally defined as $2S + 1$ where $S$ is the total spin.
From what I understand, the multiplicity corresponds with the number of unpaired/paired electrons. For example, in ...
- 21
5
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1
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289
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Why are steric effects repulsive?
Normally, I think about orbitals interacting in the context of bonding. When two atomic orbitals overlap, they can do so in-phase or out-of-phase. The in-phase overlap results in a bonding molecular ...
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2
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Confusion regarding orbital, electron and Quantum no’s [closed]
Now , In some textbook I have read that orbital is nothing but the shape of electron . s,p,d orbitals etc.
So , after knowing shape of an orbital . I got to know that inside the orbital is an electron ...
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4
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275
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What are "Secondary Orbital Interactions" in Organic Chemistry? [closed]
We used these to analyze the stability of molecules in an Organic Chemistry Course.
My teacher analyses the stability of compounds on 3 levels:
Atom level by studying the hybridization of the main ...
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6
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144
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How do bonds rotate in pericyclic reactions?
In Pericyclic reactions, it is shown that the terminal bonds rotate (conrotation or disrotation) to allow for allignment of the FMO's, thereby forming the sigma bond
However, a detail that most of my ...
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280
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Help determining normalisation constant in SALC of methane
We have been told that a symmetry adapted combination of four hydrogen orbitals is used to create localised hydrogen orbitals for methane. These orthonormal combinations are denoted ψa1, ψt’2, ψt’’2 ...
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207
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How to read character table?
I am having some problems reading character table. I will describe what I understand and thought to be right.
Consider the $\pi$ MOs formed from overlap of p-orbitals in benzene.
These two degenerate $...
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2
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2
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172
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Insight into covalent bonds from electrostatic perspective
I try to understand, from the electromagnetic side only, how the molecule could be more stable than each atom, and concluded that it could not. Where is my mistake?
Here is an illustration :
By using ...
4
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0
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93
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Symmetry Operation on Product of Functions
In regards to direct product representations, I'm trying to find a proof for:
$R(X_iY_j)=R(X_i)R(Y_j)$
Where $R$ is a symmetry operation of a group and $X_i$ and $Y_j$ are members of different basis ...
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4
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2
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6k
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Why is the first ionization enthalpy of molecular O2 less than atomic O?
A cousin of mine asked for my help to answer one of his homework questions. It stated-
Explain why- The first ionization energy of molecular oxygen $\ce{O2}$ ($\pu{1175 kJ mol-1}$), is lesser than ...
- 1,189
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0
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692
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How is Pi antibonding orbital more polar than Pi bonding orbital?
While reading about the solvent effect on electronic transition in ESR spectroscopy, I found it written somewhere that the pi anti-bonding orbitals are more polar compared to pi bonding orbitals.
Can ...
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4
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0
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476
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Symmetry Adapted molecular orbitals of Formaldehyde
I am currently trying to find the Symmetry Adapted linear Combinations (SALCs) of Formaldehyde $\ce{H2C=O}$, and use the 1s orbitals on the hydrogen atoms, and 2s, 2px, 2py and 2pz orbitals on the ...
4
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1
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674
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Overlap integrals in Hückel theory
In Hückel theory we are only interested in π systems, where $\mathrm p_z$ orbitals overlap. One of the approximations in Hückel theory is that the overlapping $\mathrm p_z$ orbitals are orthonormal:
$...
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4
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1
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1k
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How do we obtain the π molecular orbitals for allene via Hückel theory?
For a conjugated system, for instance 1,3-butadiene, we can try to obtain the π molecular orbital energies and wavefunctions via Hückel theory. In our given molecule, there are 4 interacting Pz ...
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4
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0
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761
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Molecular orbital diagram for I₃⁺ cation
Do I need to go through the whole process of reducible representations/projection operator method to come up with the bent SALCs for the $\ce{[I3]+}$ molecule? Or is it simpler than that?
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4
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1
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328
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How are molecular orbitals obtained in quantum chemistry?
When trying to solve for a molecule's molecular orbitals, we start off with the total molecular hamiltonian. However, given the difficulty of solving the Schrödinger Equation for this complicated ...
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6
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1
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Why is the carbon monoxide triple bond stronger than the nitrogen-nitrogen triple bond?
The $\ce{CO}$ triple bond has a bond enthalpy of 1072 kJ/mol while the $\ce{N2}$ triple bond has a bond enthalpy of 945 kJ/mol, at least according to my source. The molecules are isoelectronic, so I ...
- 509
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0
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28
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CO2 dynamics-vector correlations [closed]
I would like to ask if anyone has any information (schematic diagram)of vector correlations for CO2 molecule. (Is it bending in the excited state with μ in plane? How CO fragment can be ejected after ...
- 11
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0
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229
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What is the purpose of phase matching when drawing a MO diagram?
During the lecture, we were learning how to draw the MO diagram for $\mathrm{BF_3}$.
I understand that only orbitals with the same symmetry labels can interact and form molecular orbitals. My ...
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0
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35
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Properties that probe electron kinetic energy
This post is inspired by a question regarding the meaning of off-diagonal elements of the KE matrix (in some AO basis). One answer suggests that a diagonalized KE matrix might not be very useful. I ...
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7
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Why is a LCAO necessary within Hartree Fock?
As I understand it, the electronic Schrödinger equation cannot be solved for polyelectronic systems. To circumvent this problem in the Hartree-Fock method, it is assumed that the polyelectronic ...
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Linear Combination of Atomic Orbitals
In Atkins Physical Chemistry 10th edition in chapter number 10B it is given that within the Born-Oppenheimer approximation, the Schrödinger equation can be solved for the molecular species $\ce{H2+}$ ...
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6
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883
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Why do electrons in sigma bonds have zero orbital angular momentum about the internuclear axis?
As per the title, why do electrons in σ-bonds have zero orbital angular momentum about the internuclear axis?
As far as I know, the outermost electrons participate in bonding. Suppose that the 3p ...
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0
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231
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Rotational barrier of biphenyl in ground and excited electronic states
I'm studying how the energy of biphenyl varies with its dihedral angle. I know how to describe the dependence quantitatively, but still, I don't know how to explain why the rotational barrier of ...
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4
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0
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307
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Oscillator strength of a transition
I am trying to compute the oscillator strength in a molecule. Therefore I've got its Energy level values plus both wave functions $\Psi_i$ and $\Psi_j$ for the transition I want to calculate the ...
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3
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0
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281
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Hückel method for biphenyl
I am trying to calculate the energy levels of biphenyl (see picture below) using Hückel method. Since this is my first time using Hückel I am a little confused.
Biphenyl has 12 carbon atoms, ...
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174
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How to calculate a molecule's oscillator strength?
I was wondering how to calculate a molecule's (e.g. biphenyl) oscillator strength using a very simplified model.
If I want to calculate a molecule's excited states a good start is something like a ...
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3
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Is it possible to have negative bond orders?
In the MO theory, is it possible to have a molecule with bond order less than 0? The least bond order I have come across as of now is 0 (for di-atomic noble gases), indicating that the molecule cannot ...
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2
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892
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Can orbitals in a molecule be occupied via excitation like they can in atomic orbitals?
I am facing a conundrum in the way I am viewing molecule orbitals due to the existence of excited states. What I wanted to know is, since atomic orbitals can exist in excited states (i.e. you get ...
2
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1
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113
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Isn't the dual behaviour of subatomic particles contradictory?
I recently came across Molecular Orbital Theory. In this, if two electrons are bonding, their waves merge and they form a proper bond. But this is directly opposite to the particle theory, according ...
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